Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Fredholm Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions of Type Wed, 27 May 2015 09:05:14 +0000 We study Fredholm (weighted) composition operators between general weighted Banach spaces of analytic functions on the open unit disc with sup-norms. M. Carmen Gómez-Collado and David Jornet Copyright © 2015 M. Carmen Gómez-Collado and David Jornet. All rights reserved. On Pointwise Approximation of Conjugate Functions by Some Hump Matrix Means of Conjugate Fourier Series Tue, 26 May 2015 05:50:41 +0000 The results generalizing some theorems on summability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated. W. Łenski and B. Szal Copyright © 2015 W. Łenski and B. Szal. All rights reserved. A Local Estimate for the Maximal Function in Lebesgue Spaces with EXP-Type Exponents Thu, 21 May 2015 12:51:46 +0000 It is proven that if in a bounded domain and if for some , then given , the Hardy-Littlewood maximal function of , , is such that . Because , the thesis is slightly weaker than for some . The assumption that for some is proven to be optimal in the framework of the Orlicz spaces to obtain in the same class of spaces. Alberto Fiorenza Copyright © 2015 Alberto Fiorenza. All rights reserved. Fixed Point Theorems with Applications to the Solvability of Operator Equations and Inclusions on Function Spaces Wed, 20 May 2015 13:36:23 +0000 Nawab Hussain, Jesus Garcia-Falset, Mohamed-Aziz Taoudi, and Calogero Vetro Copyright © 2015 Nawab Hussain et al. All rights reserved. Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems Wed, 20 May 2015 08:26:57 +0000 Hemant Kumar Nashine, Mujahid Abbas, Marlène Frigon, and Calogero Vetro Copyright © 2015 Hemant Kumar Nashine et al. All rights reserved. Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities Tue, 19 May 2015 11:32:44 +0000 We introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepest-descent method, and Mann’s iteration method. We prove that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions, and the solution set of general system of variational inequalities (GSVI), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm for solving a hierarchical variational inequality problem with constraints of finitely many GMEPs, finitely many variational inclusions, and the GSVI. The results obtained in this paper improve and extend the corresponding results announced by many others. L. C. Ceng, A. Latif, C. F. Wen, and A. E. Al-Mazrooei Copyright © 2015 L. C. Ceng et al. All rights reserved. A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition Tue, 19 May 2015 11:31:16 +0000 We establish a new Lyapunov-type inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain Mittag-Leffler functions has no real zeros. Mohamed Jleli, Lakhdar Ragoub, and Bessem Samet Copyright © 2015 Mohamed Jleli et al. All rights reserved. Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function Tue, 19 May 2015 08:28:44 +0000 We are concerned with the following third-order boundary value problem with integral boundary condition:      where , and . Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained. Bing-Wei Niu, Jian-Ping Sun, and Qiu-Yan Ren Copyright © 2015 Bing-Wei Niu et al. All rights reserved. Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces Tue, 19 May 2015 07:31:25 +0000 This paper investigates properties of convergence of distances of -cyclic contractions on the union of the subsets of an abstract set defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of -cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the -composite mappings restricted to each of the subsets in the cyclic disposal are also investigated and some illustrative examples are given. Manuel De la Sen and Erdal Karapınar Copyright © 2015 Manuel De la Sen and Erdal Karapınar. All rights reserved. Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems Mon, 18 May 2015 13:22:52 +0000 We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem. Shu-qiang Shan, Yu Han, and Nan-jing Huang Copyright © 2015 Shu-qiang Shan et al. All rights reserved. Existence of Positive Solutions for a Fourth-Order -Point Boundary Value Problem Mon, 18 May 2015 12:06:52 +0000 By using Krasnosel’skii’s fixed point theorem and the fixed point index theorem in the special function space, we obtain some sufficient conditions for the existence of positive solutions of fourth-order boundary value problem with multipoint boundary conditions. Applications of our results to some special problems are also discussed. Liu Yang and Chunfang Shen Copyright © 2015 Liu Yang and Chunfang Shen. All rights reserved. Common Fixed Point of Two -Weakly Commuting Mappings in -Metric Spaces Mon, 18 May 2015 12:06:27 +0000 We prove some common fixed point results for two mappings satisfying generalized contractive condition in -metric space. Note that -metric of main results in this work are not necessarily continuous. So our results extend and improve several previous works. We also present one example that shows the applicability and usefulness of our results. Poom Kumam, Wutiphol Sintunavarat, Shaban Sedghi, and Nabi Shobkolaei Copyright © 2015 Poom Kumam et al. All rights reserved. Boundary Value Problems of Fractional Order Differential Equation with Integral Boundary Conditions and Not Instantaneous Impulses Mon, 18 May 2015 12:03:25 +0000 We investigate the existence of mild solutions for fractional order differential equations with integral boundary conditions and not instantaneous impulses. By some fixed-point theorems, we establish sufficient conditions for the existence and uniqueness of solutions. Finally, two interesting examples are given to illustrate our theory results. Peiluan Li and Changjin Xu Copyright © 2015 Peiluan Li and Changjin Xu. All rights reserved. Some Generalized Difference Sequence Spaces Defined by a Sequence of Moduli in -Normed Spaces Mon, 18 May 2015 11:48:57 +0000 We introduce some new generalized difference sequence spaces by means of ideal convergence, infinite matrix, and a sequence of modulus functions over -normed spaces. We also make an effort to study several properties relevant to topological, algebraic, and inclusion relations between these spaces. Abdullah Alotaibi, Kuldip Raj, and S. A. Mohiuddine Copyright © 2015 Abdullah Alotaibi et al. All rights reserved. On the Generalized Ulam-Hyers-Rassias Stability of Quadratic Mappings in Modular Spaces without -Conditions Mon, 18 May 2015 10:49:31 +0000 We approach the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives of -conditions. Kittipong Wongkum, Parin Chaipunya, and Poom Kumam Copyright © 2015 Kittipong Wongkum et al. All rights reserved. New Dependent Fixed Point Theorems for Suzuki Type -Contractions Mon, 18 May 2015 10:23:20 +0000 We introduce new concepts of an -GF-contractive nonself-mapping, a weak -GF-contractive nonself-mapping, a generalized -GF-contractive nonself-mapping, and Suzuki type GF-contractions and establish the existence of PPF dependent fixed point theorems for such kind of contractive nonself-mappings in the Razumikhin class. As applications of our results, we derive some PPF dependent fixed point theorems for GF-contractive nonself-mappings whenever the range space is endowed with a graph or a partial order. The obtained results generalize, extend, and modify some PPF dependent fixed point results in the literature. M. A. Kutbi, N. Hussain, and S. Khaleghizadeh Copyright © 2015 M. A. Kutbi et al. All rights reserved. On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces Mon, 18 May 2015 09:54:18 +0000 The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented. Renu Chugh, Preety Malik, and Vivek Kumar Copyright © 2015 Renu Chugh et al. All rights reserved. Caristi’s Fixed Point Theorem and Subrahmanyam’s Fixed Point Theorem in -Generalized Metric Spaces Mon, 18 May 2015 08:56:55 +0000 We discuss the completeness of -generalized metric spaces in the sense of Branciari. We also prove generalizations of Subrahmanyam’s and Caristi’s fixed point theorem. Badriah Alamri, Tomonari Suzuki, and Liaqat Ali Khan Copyright © 2015 Badriah Alamri et al. All rights reserved. On the Approximate Controllability of Fractional Evolution Equations with Generalized Riemann-Liouville Fractional Derivative Mon, 18 May 2015 08:36:34 +0000 We discuss the approximate controllability of fractional evolution equations involving generalized Riemann-Liouville fractional derivative. The results are obtained with the help of the theory of fractional calculus, semigroup theory, and the Schauder fixed point theorem under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the abstract theory. N. I. Mahmudov and M. A. McKibben Copyright © 2015 N. I. Mahmudov and M. A. McKibben. All rights reserved. An Approximation Method for Solving Volterra Integrodifferential Equations with a Weighted Integral Condition Wed, 13 May 2015 06:37:46 +0000 We apply the reproducing kernel Hilbert space (RKHS) method for getting analytical and approximate solutions for second-order hyperbolic integrodifferential equations with a weighted integral condition. The analytical solution is represented in the form of series; thus, the n-terms approximate solutions are obtained. The results of the numerical examples are compared with the exact solutions to illustrate the accuracy and the effectivity of this method. A. Guezane-Lakoud, N. Bendjazia, and R. Khaldi Copyright © 2015 A. Guezane-Lakoud et al. All rights reserved. Some Discussions on the Difference Equation Sun, 10 May 2015 09:32:11 +0000 We give in this work the sufficient conditions on the positive solutions of the difference equation ,  , where α, k, and under positive initial conditions ,   to be bounded, α-convergent, the equilibrium point to be globally asymptotically stable and that every positive solution converges to a prime two-periodic solution. Our results coincide with that known for the cases of Amleh et al. (1999) and of Hamza and Morsy (2009). We offer improving conditions in the case of of Gümüs and Öcalan (2012) and explain our results by some numerical examples with figures. Awad A. Bakery Copyright © 2015 Awad A. Bakery. All rights reserved. Positive Coexistence of Steady States for a Diffusive Ratio-Dependent Predator-Prey Model with an Infected Prey Wed, 06 May 2015 12:01:57 +0000 We examine a diffusive ratio-dependent predator-prey system with disease in the prey under homogeneous Dirichlet boundary conditions with a hostile environment at its boundary. We investigate the positive coexistence of three interacting species (susceptible prey, infected prey, and predator) and provide nonexistence conditions of positive solutions to the system. In addition, the global stability of the trivial and semitrivial solutions to the system is studied. Furthermore, the biological interpretation based on the result is also presented. The methods are employed from a comparison argument for the elliptic problem as well as the fixed-point theory as applied to a positive cone on a Banach space. Kwangjoong Kim and Inkyung Ahn Copyright © 2015 Kwangjoong Kim and Inkyung Ahn. All rights reserved. Approximative Compactness and Radon-Nikodym Property in Nearly Dentable Banach Spaces and Applications Wed, 06 May 2015 09:41:31 +0000 Authors define nearly dentable Banach space. Authors study Radon-Nikodym property, approximative compactness and continuity metric projector operator in nearly dentable space. Moreover, authors obtain some examples of nearly dentable space in Orlicz function spaces. Finally, by the method of geometry of Banach spaces, authors give important applications of nearly dentability in generalized inverse theory of Banach space. Shaoqiang Shang and Yunan Cui Copyright © 2015 Shaoqiang Shang and Yunan Cui. All rights reserved. Sharp Power Mean Bounds for the One-Parameter Harmonic Mean Thu, 30 Apr 2015 18:45:29 +0000 We present the best possible parameters and such that the double inequality holds for all and with , where    and and are the power and one-parameter harmonic means of and , respectively. Yu-Ming Chu, Li-Min Wu, and Ying-Qing Song Copyright © 2015 Yu-Ming Chu et al. All rights reserved. Solitary Waves of the Schrödinger Lattice System with Nonlinear Hopping Wed, 29 Apr 2015 08:55:51 +0000 This paper is concerned with the nonlinear Schrödinger lattice with nonlinear hopping. Via variation approach and the Nehari manifold argument, we obtain two types of solution: periodic ground state and localized ground state. Moreover, we consider the convergence of periodic solutions to the solitary waves. Ming Cheng Copyright © 2015 Ming Cheng. All rights reserved. Iterative Methods for Nonconvex Equilibrium Problems in Uniformly Convex and Uniformly Smooth Banach Spaces Tue, 28 Apr 2015 14:00:54 +0000 We suggest and study the convergence of some new iterative schemes for solving nonconvex equilibrium problems in Banach spaces. Many existing results have been obtained as particular cases. Messaoud Bounkhel Copyright © 2015 Messaoud Bounkhel. All rights reserved. Generalized Fractional Integral Operators on Generalized Local Morrey Spaces Wed, 22 Apr 2015 06:23:08 +0000 We study the continuity properties of the generalized fractional integral operator on the generalized local Morrey spaces and generalized Morrey spaces . We find conditions on the triple which ensure the Spanne-type boundedness of from one generalized local Morrey space to another , , and from to the weak space , . We also find conditions on the pair which ensure the Adams-type boundedness of from to for and from to for . In all cases the conditions for the boundedness of are given in terms of Zygmund-type integral inequalities on and , which do not assume any assumption on monotonicity of , , and in . V. S. Guliyev, A. F. Ismayilova, A. Kucukaslan, and A. Serbetci Copyright © 2015 V. S. Guliyev et al. All rights reserved. Hardy-Littlewood-Sobolev Inequalities on -Adic Central Morrey Spaces Wed, 22 Apr 2015 06:19:59 +0000 We establish the Hardy-Littlewood-Sobolev inequalities on -adic central Morrey spaces. Furthermore, we obtain the -central BMO estimates for commutators of -adic Riesz potential on -adic central Morrey spaces. Qing Yan Wu and Zun Wei Fu Copyright © 2015 Qing Yan Wu and Zun Wei Fu. All rights reserved. Characterization Theorems for Generalized Functionals of Discrete-Time Normal Martingale Sun, 19 Apr 2015 10:42:18 +0000 We aim at characterizing generalized functionals of discrete-time normal martingales. Let be a discrete-time normal martingale that has the chaotic representation property. We first construct testing and generalized functionals of with an appropriate orthonormal basis for ’s square integrable functionals. Then we introduce a transform, called the Fock transform, for these functionals and characterize them via the transform. Several characterization theorems are established. Finally we give some applications of these characterization theorems. Our results show that generalized functionals of discrete-time normal martingales can be characterized only by growth condition, which contrasts sharply with the case of some continuous-time processes (e.g., Brownian motion), where both growth condition and analyticity condition are needed to characterize generalized functionals of those continuous-time processes. Caishi Wang and Jinshu Chen Copyright © 2015 Caishi Wang and Jinshu Chen. All rights reserved. Some Classes of Function Spaces, Their Properties, and Their Applications 2014 Wed, 08 Apr 2015 06:56:05 +0000 Józef Banaś, Janusz Matkowski, Nelson Merentes, Jose Luis Sanchez, and Kishin Sadarangani Copyright © 2015 Józef Banaś et al. All rights reserved.